convolution

Discrete-time convolution product of \(f\) and \(g\)
(See definition 2.2 p. 20)

Performs parametric and non-parametric estimation and simulation
for multi-state discrete-time semi-Markov processes. For the parametric
estimation, several discrete distributions are considered for the sojourn
times: Uniform, Geometric, Poisson, Discrete Weibull and Negative Binomial.
The non-parametric estimation concerns the sojourn time distributions,
where no assumptions are done on the shape of distributions. Moreover, the
estimation can be done on the basis of one or several sample paths, with or
without censoring at the beginning or/and at the end of the sample paths.
Reliability indicators such as reliability, maintainability, availability,
BMP-failure rate, RG-failure rate, mean time to failure and mean time to
repair are available as well. The implemented methods are described in
Barbu, V.S., Limnios, N. (2008) <doi:10.1007/978-0-387-73173-5>,
Barbu, V.S., Limnios, N. (2008) <doi:10.1080/10485250701261913> and
Trevezas, S., Limnios, N. (2011) <doi:10.1080/10485252.2011.555543>.
Estimation and simulation of discrete-time k-th order Markov chains are
also considered.

Nicolas Vergne

smmR

Simulation, Estimation and Reliability of Semi-Markov Models

Vlad Stefan Barbu

Florian Lecocq

Corentin Lothode

convolution function

<dl><dt>f</dt>
<dd>A vector giving the values of the function \(f\) for each
\(k \in N\).</dd>
<dt>g</dt>
<dd>A vector giving the values of the function \(g\) for each
\(k \in N\).</dd></dl>

Arguments

Discrete-time convolution product of \(f\) and \(g\)
(See definition 2.2 p. 20) — convolution

<dl>

<dt>f</dt>
<dd>A vector giving the values of the function \(f\) for each
\(k \in N\).</dd>


<dt>g</dt>
<dd>A vector giving the values of the function \(g\) for each
\(k \in N\).</dd>

</dl>

convolution: Discrete-time convolution product of \(f\) and \(g\) (See definition 2.2 p. 20)

Description

Usage

Value

Arguments